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SageMath
sage: E = EllipticCurve("b1")
sage: E.isogeny_class()
Elliptic curves in class 303450.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 303450.b1 | 303450b6 | [1, 1, 0, -12590140650, -543747958852500] | [2] | 509607936 | |
| 303450.b2 | 303450b3 | [1, 1, 0, -1825179650, 30007268392500] | [2] | 254803968 | |
| 303450.b3 | 303450b4 | [1, 1, 0, -794027650, -8334185895500] | [2, 2] | 254803968 | |
| 303450.b4 | 303450b2 | [1, 1, 0, -125859650, 366029632500] | [2, 2] | 127401984 | |
| 303450.b5 | 303450b1 | [1, 1, 0, 22108350, 38872384500] | [2] | 63700992 | \(\Gamma_0(N)\)-optimal |
| 303450.b6 | 303450b5 | [1, 1, 0, 311397350, -29720843370500] | [2] | 509607936 |
Rank
sage: E.rank()
The elliptic curves in class 303450.b have rank \(1\).
Complex multiplication
The elliptic curves in class 303450.b do not have complex multiplication.Modular form 303450.2.a.b
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 8 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 2 & 4 & 1 & 2 & 4 & 2 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 8 & 4 & 4 & 2 & 1 & 8 \\ 4 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
